TY - JOUR
T1 - The Error-Minimization-Based Strategy for Moving Mesh Methods
AU - K. Lipnikov & M. Shashkov
JO - Communications in Computational Physics
VL - 1
SP - 53
EP - 80
PY - 2006
DA - 2006/01
SN - 1
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cicp/7950.html
KW - 
AB - <p style="text-align: justify;">The typical elements in a numerical simulation of fluid flow using moving meshes
are a time integration scheme, a rezone method in which a new mesh is defined, and a remapping
(conservative interpolation) in which a solution is transferred to the new mesh. The
objective of the rezone method is to move the computational mesh to improve the robustness,
accuracy and eventually efficiency of the simulation. In this paper, we consider the one-dimensional
viscous Burgers&#39; equation and describe a new rezone strategy which minimizes
the <em>L</em><sub>2</sub> norm of error and maintains mesh smoothness. The efficiency of the proposed method
is demonstrated with numerical examples.</p>